krige {gstat}R Documentation

Simple, Ordinary or Universal, global or local, Point or Block Kriging

Description

Function for simple, ordinary or universal kriging (sometimes called external drift kriging), kriging in a local neighbourhood, point kriging or kriging of block mean values (rectangular or irregular blocks), and conditional (Gaussian or indicator) simulation equivalents for all kriging varieties.

Usage

 krige(formula, locations, data, newdata, model, beta, nmax = Inf,
nmin = 0, maxdist = Inf, block, nsim = 0, indicators = FALSE, 
na.action = na.pass, ...) 

Arguments

formula formula that defines the dependent variable as a linear model of independent variables; suppose the dependent variable has name z, for ordinary and simple kriging use the formula z~1; for simple kriging also define beta (see below); for universal kriging, suppose z is linearly dependent on x and y, use the formula z~x+y
locations formula with only independent variables that define the spatial data locations (coordinates), e.g. ~x+y; if data is of class spatial.data.frame, this argument may be ignored, as it can be derived from the data
data data frame; should contain the dependent variable, independent variables, and coordinates.
newdata data frame with prediction/simulation locations; should contain columns with the independent variables (if present) and the coordinates with names as defined in locations
model variogram model of dependent variable (or its residuals), defined by a call to vgm or fit.variogram
beta only for simple kriging (and simulation based on simple kriging); vector with the trend coefficients (including intercept); if no independent variables are defined the model only contains an intercept and this should be the simple kriging mean
nmax for local kriging: the number of nearest observations that should be used for a kriging prediction or simulation, where nearest is defined in terms of the space of the spatial locations. By default, all observations are used
nmin for local kriging: if the number of nearest observations within distance maxdist is less than nmin, a missing value will be generated; see maxdist
maxdist for local kriging: only observations within a distance of maxdist from the prediction location are used for prediction or simulation; if combined with nmax, both criteria apply
block block size; a vector with 1, 2 or 3 values containing the size of a rectangular in x-, y- and z-dimension respectively (0 if not set), or a data frame with 1, 2 or 3 columns, containing the points that discretize the block in the x-, y- and z-dimension; the latter can be used to define irregular blocks. By default, predictions or simulations refer to point support values.
nsim integer; if set to a non-zero value, conditional simulation is used instead of kriging interpolation. For this, sequential Gaussian or indicator simulation is used (depending on the value of indicators), following a single random path through the data.
indicators logical, only relevant if nsim is non-zero; if TRUE, use indicator simulation; else use Gaussian simulation
na.action function determining what should be done with missing values in 'newdata'. The default is to predict 'NA'. Missing values in coordinates and predictors are both dealt with.
... other arguments that will be passed to gstat

Details

This function is a simple wrapper function around gstat and predict.gstat for univariate kriging prediction and conditional simulation methods available in gstat. For multivariate prediction or simulation, or for other interpolation methods provided by gstat (such as inverse distance weighted interpolation or trend surface interpolation) use the functions gstat and predict.gstat directly.

For further details, see predict.gstat.

Value

a data frame containing the coordinates of newdata, and columns of prediction and prediction variance (in case of kriging) or the abs(nsim) columns of the conditional Gaussian or indicator simulations

Note

Daniel G. Krige is a South African scientist who was a mining engineer when he first used generalised least squares prediction with spatial covariances in the 50's. George Matheron coined the term kriging in the 60's for the action of doing this, although very similar approaches had been taken in the field of meteorology. Beside being Krige's name, I consider "krige" to be to "kriging" what "predict" is to "prediction".

Author(s)

Edzer J. Pebesma

References

N.A.C. Cressie, 1993, Statistics for Spatial Data, Wiley.

http://www.gstat.org/

Pebesma, E.J., 2004. Multivariable geostatistics in S: the gstat package. Computers & Geosciences, 30: 683-691.

See Also

gstat, predict.gstat

Examples

data(meuse)
data(meuse.grid)
m <- vgm(.59, "Sph", 874, .04)
# ordinary kriging:
x <- krige(log(zinc)~1, ~x+y, model = m, data = meuse, newd = meuse.grid)
levelplot(var1.pred~x+y, x, aspect = mapasp(x),
        main = "ordinary kriging predictions")
levelplot(var1.var~x+y, x, aspect = mapasp(x),
        main = "ordinary kriging variance")
# simple kriging:
x <- krige(log(zinc)~1, ~x+y, model = m, data = meuse, newdata = meuse.grid, 
        beta=5.9)
# residual variogram:
m <- vgm(.4, "Sph", 954, .06)
# universal block kriging:
x <- krige(log(zinc)~x+y, ~x+y, model = m, data = meuse, newdata = 
        meuse.grid, block = c(40,40))
levelplot(var1.pred~x+y, x, aspect = mapasp(x),
        main = "universal kriging predictions")
levelplot(var1.var~x+y, x, aspect = mapasp(x),
        main = "universal kriging variance")

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